Paper: arXiv 2411.05951

Abstract

Multifractality is a concept that helps compactly grasping the most essential features of the financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on the centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from June 6, 2023, to June 30, 2024, the present study using Multifractal Detrended Fluctuation Analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges convincing traces of multifractality are already emerging on this new trading as well. The resulting multifractal spectra are however strongly left-side asymmetric which indicates that this multifractality comes primarily from large fluctuations and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events a trace of multifractal cross-correlations between the two characteristics is also observed.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper uses advanced multifractal analysis (MFDFA) and discusses asymmetric spectra and cross-correlations, indicating high mathematical complexity. It employs a large, real-world dataset (tick-by-tick transactions from Uniswap over a year) and performs statistical tests, demonstrating strong empirical implementation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Detect multifractality<br>in decentralized crypto trading"] --> B["Data Source<br>Uniswap Universal Router<br>Tick-by-tick transactions"]
  B --> C["Parameters<br>June 6, 2023 - June 30, 2024<br>Volume & Returns"]
  C --> D["Methodology<br>Multifractal Detrended<br>Fluctuation Analysis MFDFA"]
  D --> E["Computation<br>Extract Multifractal<br>Spectra & Scaling Exponents"]
  E --> F{"Outcome"}
  F --> G["Key Finding 1<br>Multifractality present in DEX<br>but left-side asymmetric<br>driven by large fluctuations"]
  F --> H["Key Finding 2<br>Multifractality stronger<br>in Volume series than Returns"]

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